What is a PRP ?
A PRP is a probable prime number, a number that nobody knows how to prove
or disprove its primality.
Here are some criterions that can be used to recognize these numbers
:
- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N
should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3.
N should pass the strong test in base b.
- or more (if someone has got an idea) !!!
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
9751 | 10^90661+2373 | 90662 | Patrick De Geest | 11/2018 |
9752 | 10^90661-194781 | 90661 | Patrick De Geest | 07/2019 |
9753 | 3*5^129698+8 | 90656 | Lelio R Paula | 10/2014 |
9754 | F(433781) | 90655 | Henri Lifchitz | 09/2003 |
9755 | 19^70891+82 | 90653 | Lelio R Paula | 06/2016 |
9756 | (29*2^301124-1)/13 | 90648 | Lelio R Paula | 02/2014 |
9757 | 10^90636+64159 | 90637 | Patrick De Geest | 07/2019 |
9758 | 10^90636-3101 | 90636 | Patrick De Geest | 11/2018 |
9759 | 7*3^189953-8 | 90632 | Lelio R Paula | 08/2014 |
9760 | 10^90626+339289 | 90627 | Patrick De Geest | 07/2019 |
9761 | 10^90626-1131 | 90626 | Patrick De Geest | 11/2018 |
9762 | 11^87022-1800 | 90625 | Enzo Doria | 12/2012 |
9763 | 10^90623+861 | 90624 | Patrick De Geest | 11/2018 |
9764 | 10^90623-305841 | 90623 | Patrick De Geest | 07/2019 |
9765 | (2^301042+47)/12036969 | 90616 | Lelio R Paula | 06/2013 |
9766 | 2^301004-2786939 | 90612 | Enzo Doria | 03/2016 |
9767 | 10^90611+169977 | 90612 | Patrick De Geest | 07/2019 |
9769 | 10^90611-9737 | 90611 | Patrick De Geest | 11/2018 |
9768 | 10^90610+36747 | 90611 | Patrick De Geest | 07/2019 |
9770 | 10^90609+6823 | 90610 | Patrick De Geest | 11/2018 |
9771 | 10^90610-26573 | 90610 | Patrick De Geest | 07/2019 |
9772 | 10^90609-228173 | 90609 | Patrick De Geest | 07/2019 |
9773 | 2^300980-27 | 90605 | Lelio R Paula | 11/2012 |
9774 | 2*10^90597-7 | 90598 | Dmitry Domanov | 11/2010 |
9775 | 197^39485+2 | 90597 | Lelio R Paula | 06/2013 |
9776 | 7^107198+48 | 90593 | Lelio R Paula | 04/2016 |
9777 | (86*10^90588+121)/9 | 90589 | Robert Price | 03/2017 |
9778 | 2^300923+53 | 90587 | Lelio R Paula | 11/2012 |
9779 | 2^300874+7 | 90573 | Lelio R Paula | 10/2012 |
9780 | 10^90567+9489 | 90568 | Patrick De Geest | 11/2018 |
9781 | 10^90567-231353 | 90567 | Patrick De Geest | 07/2019 |
9782 | (2^300857+2214)/2 | 90567 | Stefano Morozzi | 01/2020 |
9783 | 5^129568-56 | 90565 | Lelio R Paula | 04/2016 |
9784 | 2^300847-112831 | 90564 | Enzo Doria | 06/2014 |
9785 | 10^90562+790197 | 90563 | Patrick De Geest | 07/2019 |
9786 | 10^90562-2981 | 90562 | Patrick De Geest | 11/2018 |
9787 | (7796^23269-1)/7795 | 90557 | Serge Batalov | 08/2020 |
9788 | (31*10^90554+257)/9 | 90555 | Robert Price | 12/2021 |
9789 | 10^90549+3811 | 90550 | Patrick De Geest | 11/2018 |
9790 | 10^90549-630303 | 90549 | Patrick De Geest | 07/2019 |
9791 | 2^300790-4541 | 90547 | Yves Minet | 03/2019 |
9792 | 10^90532+8169 | 90533 | Patrick De Geest | 11/2018 |
9793 | 10^90531+9831 | 90532 | Patrick De Geest | 11/2018 |
9794 | 10^90532-154889 | 90532 | Patrick De Geest | 07/2019 |
9795 | 10^90531-1060589 | 90531 | Patrick De Geest | 07/2019 |
9797 | 2^300718+255255 | 90526 | Lelio R Paula | 02/2016 |
9796 | (2^300719+938)/2 | 90526 | Stefano Morozzi | 01/2020 |
9798 | 10^90516+215917 | 90517 | Patrick De Geest | 07/2019 |
9799 | 10^90516-6783 | 90516 | Patrick De Geest | 11/2018 |
9800 | 10^90511+30177 | 90512 | Patrick De Geest | 07/2019 |
9801 | 10^90511-6977 | 90511 | Patrick De Geest | 11/2018 |
9802 | (8573^23011-1)/8572 | 90502 | Serge Batalov | 08/2020 |
9803 | 2^300637+95 | 90501 | Lelio R Paula | 11/2012 |
9804 | 7^107087-24 | 90500 | Lelio R Paula | 04/2016 |
9805 | 10^90499+191547 | 90500 | Patrick De Geest | 07/2019 |
9806 | 10^90499-5823 | 90499 | Patrick De Geest | 11/2018 |
9808 | (10^90499+3^90499)/13 | 90498 | Robert Price | 01/2013 |
9807 | 13^81241+90 | 90498 | Lelio R Paula | 06/2016 |
9809 | (2^300600+1222)/2 | 90490 | Stefano Morozzi | 01/2020 |
9810 | 10^90480+5131 | 90481 | Patrick De Geest | 11/2018 |
9811 | 10^90480-85721 | 90480 | Patrick De Geest | 07/2019 |
9812 | (34*10^90478-547)/9 | 90479 | Robert Price | 03/2021 |
9813 | 6^116273-85 | 90478 | Lelio R Paula | 05/2016 |
9814 | 10^90473+3139 | 90474 | Patrick De Geest | 11/2018 |
9815 | 10^90473-150599 | 90473 | Patrick De Geest | 07/2019 |
9816 | 10^90470+2319 | 90471 | Patrick De Geest | 11/2018 |
9817 | 10^90470-71637 | 90470 | Patrick De Geest | 07/2019 |
9818 | 6^116256-17573 | 90465 | Enzo Doria | 02/2013 |
9819 | 2^300502+54615 | 90461 | Lelio R Paula | 02/2016 |
9820 | (13*2^300487+1)/45 | 90456 | Lelio R Paula | 09/2013 |
9821 | 10^90453+141843 | 90454 | Patrick De Geest | 07/2019 |
9823 | 10^90453-3969 | 90453 | Patrick De Geest | 11/2018 |
9822 | 10^90452+59317 | 90453 | Patrick De Geest | 05/2021 |
9824 | 10^90452-80000001 | 90452 | Robert Price | 04/2021 |
9825 | 10^90452-84713 | 90452 | Patrick De Geest | 05/2021 |
9826 | 10^90440+1359 | 90441 | Patrick De Geest | 11/2018 |
9827 | 10^90440-18821 | 90440 | Patrick De Geest | 07/2019 |
9828 | (3^189545-8)/5 | 90436 | Lelio R Paula | 01/2013 |
9829 | (7*2^300406-1)/3 | 90432 | Lelio R Paula | 02/2014 |
9830 | 10^90430+3339 | 90431 | Patrick De Geest | 11/2018 |
9831 | 10^90430-63477 | 90430 | Patrick De Geest | 07/2019 |
9832 | (5408^24223-1)/5407 | 90422 | Serge Batalov | 08/2020 |
9833 | 10^90414+229593 | 90415 | Patrick De Geest | 07/2019 |
9834 | 10^90414-1547 | 90414 | Patrick De Geest | 11/2018 |
9835 | 10^90404+47041 | 90405 | Patrick De Geest | 07/2019 |
9836 | 10^90404-6429 | 90404 | Patrick De Geest | 11/2018 |
9837 | 10^90401+2077 | 90402 | Patrick De Geest | 11/2018 |
9838 | 10^90401-368637 | 90401 | Patrick De Geest | 07/2019 |
9839 | 24900^4271+4271^24900 | 90401 | Hans Havermann | 08/2020 |
9840 | 4*5^129332+3 | 90400 | Lelio R Paula | 10/2014 |
9842 | 10^90397+19783 | 90398 | Patrick De Geest | 07/2019 |
9841 | 23380^7353+7353^23380 | 90398 | Hans Havermann | 08/2020 |
9844 | 10^90397-323 | 90397 | Patrick De Geest | 11/2018 |
9843 | (2^300293+2762)/2 | 90397 | Stefano Morozzi | 01/2020 |
9845 | 24058^5719+5719^24058 | 90394 | Hans Havermann | 08/2020 |
9846 | 2^300249-16245 | 90384 | Enzo Doria | 04/2013 |
9847 | 24414^5035+5035^24414 | 90381 | Hans Havermann | 08/2020 |
9848 | (7*10^90371-313)/9 | 90371 | Robert Price | 11/2016 |
9849 | 10^90363+58677 | 90364 | Patrick De Geest | 07/2019 |
9850 | 10^90363-3557 | 90363 | Patrick De Geest | 11/2018 |
9851 | 10^90358+104641 | 90359 | Patrick De Geest | 07/2019 |
9854 | 2*6^116118+7 | 90358 | Lelio R Paula | 10/2014 |
9853 | 10^90358-4979 | 90358 | Patrick De Geest | 11/2018 |
9852 | 10^90357+112837 | 90358 | Patrick De Geest | 07/2019 |
9855 | 10^90357-189593 | 90357 | Patrick De Geest | 07/2019 |
9856 | 10^90356+53113 | 90357 | Patrick De Geest | 07/2019 |
9857 | 10^90356-7197 | 90356 | Patrick De Geest | 11/2018 |
9858 | 10^90353+603211 | 90354 | Patrick De Geest | 07/2019 |
9859 | 10^90353-1089 | 90353 | Patrick De Geest | 11/2018 |
9860 | (24737*2^300101+1)/25 | 90343 | Lelio R Paula | 06/2014 |
9861 | 4*10^90334-21 | 90335 | Robert Price | 04/2016 |
9862 | (4546^24697-1)/4545 | 90329 | Serge Batalov | 08/2020 |
9863 | 10^90322+137691 | 90323 | Patrick De Geest | 07/2019 |
9864 | 10^90322-9551 | 90322 | Patrick De Geest | 11/2018 |
9865 | 10^90316+9991 | 90317 | Patrick De Geest | 11/2018 |
9866 | (4550^24691-1)/4549 | 90317 | Serge Batalov | 08/2020 |
9867 | 10^90316-45627 | 90316 | Patrick De Geest | 07/2019 |
9868 | 10^90315+32889 | 90316 | Patrick De Geest | 07/2019 |
9870 | 2^300019-110335 | 90315 | Enzo Doria | 05/2014 |
9869 | 10^90315-8561 | 90315 | Patrick De Geest | 11/2018 |
9871 | FAB2(300001,5032) | 90310 | Robert Price | 05/2019 |
9872 | FAB2(300001,29405) | 90310 | Robert Price | 05/2019 |
9873 | (2^299965+2774)/2 | 90299 | Stefano Morozzi | 01/2020 |
9874 | 23679^6506+6506^23679 | 90296 | Hans Havermann | 08/2020 |
9875 | 2^299949-1005 | 90294 | Lelio R Paula | 11/2013 |
9876 | (2^299947+2054)/2 | 90293 | Stefano Morozzi | 01/2020 |
9877 | 21740^14229+14229^21740 | 90291 | Hans Havermann | 08/2020 |
9878 | 10^90279+62457 | 90280 | Patrick De Geest | 07/2019 |
9879 | 10^90279-1551 | 90279 | Patrick De Geest | 09/2018 |
9880 | (2^299892+1986)/2 | 90277 | Stefano Morozzi | 01/2020 |
9881 | (2^299893+3866)/2 | 90277 | Stefano Morozzi | 01/2020 |
9882 | 2^299868-109613 | 90270 | Enzo Doria | 04/2014 |
9883 | 10^90259+359299 | 90260 | Patrick De Geest | 07/2019 |
9884 | 10^90259-9443 | 90259 | Patrick De Geest | 09/2018 |
9885 | (2^299831+3786)/2 | 90258 | Stefano Morozzi | 01/2020 |
9886 | 10^90252+102873 | 90253 | Patrick De Geest | 07/2019 |
9887 | 10^90252-8103 | 90252 | Patrick De Geest | 09/2018 |
9888 | 5*2^299799-3 | 90250 | Lelio R Paula | 08/2014 |
9889 | (2^299803+3326)/2 | 90250 | Stefano Morozzi | 01/2020 |
9890 | 13^81008-2 | 90239 | Lelio R Paula | 09/2013 |
9891 | 80697!4-256 | 90234 | Robert Price | 11/2019 |
9893 | 64^49957-63^49957 | 90232 | Robert Price | 07/2013 |
9892 | (2^299745+2994)/2 | 90232 | Stefano Morozzi | 01/2020 |
9894 | 10^90227+56281 | 90228 | Patrick De Geest | 06/2016 |
9898 | 2^299725+315 | 90227 | Lelio R Paula | 11/2013 |
9895 | 10^90227-1000000001 | 90227 | Robert Price | 05/2016 |
9896 | 10^90227-68763 | 90227 | Patrick De Geest | 06/2016 |
9897 | 9*10^90226+29 | 90227 | Robert Price | 03/2022 |
9899 | 5^129082+48 | 90225 | Lelio R Paula | 03/2016 |
9900 | 2^299699+195 | 90219 | Lelio R Paula | 10/2012 |
9901 | (55*10^90211-1)/9 | 90212 | Ray Chandler | 02/2012 |
9902 | 22131^11918+11918^22131 | 90211 | Hans Havermann | 08/2020 |
9903 | 10^90209+8971 | 90210 | Patrick De Geest | 09/2018 |
9904 | 10^90209-724797 | 90209 | Patrick De Geest | 07/2019 |
9905 | 10^90208+189531 | 90209 | Patrick De Geest | 07/2019 |
9906 | 10^90208-2247 | 90208 | Patrick De Geest | 09/2018 |
9907 | (629^32233-1)/628 | 90207 | Michael Stocker | 05/2020 |
9908 | 116^43693-115 | 90203 | Norbert Schneider | 08/2018 |
9909 | 10^90202+3553 | 90203 | Patrick De Geest | 09/2018 |
9910 | 3^189053+280 | 90202 | Lelio R Paula | 04/2016 |
9911 | 10^90202-67793 | 90202 | Patrick De Geest | 07/2019 |
9912 | 2^299639-187 | 90201 | Lelio R Paula | 10/2012 |
9913 | 10^90199+254031 | 90200 | Patrick De Geest | 07/2019 |
9914 | 10^90199-2891 | 90199 | Patrick De Geest | 09/2018 |
9916 | 2^299631+183 | 90198 | Lelio R Paula | 10/2012 |
9915 | 21567^15212+15212^21567 | 90198 | Hans Havermann | 08/2020 |
9917 | 10^90196+187539 | 90197 | Patrick De Geest | 07/2019 |
9919 | 10^90196-9683 | 90196 | Patrick De Geest | 09/2018 |
9918 | 21708^14287+14287^21708 | 90196 | Hans Havermann | 08/2020 |
9920 | 10^90193+104973 | 90194 | Patrick De Geest | 07/2019 |
9921 | 10^90193-9809 | 90193 | Patrick De Geest | 09/2018 |
9922 | (21*2^299611-1)/29 | 90192 | Lelio R Paula | 02/2014 |
9923 | (2277^26863-1)/2276 | 90186 | Serge Batalov | 08/2020 |
9924 | 2^299567+113 | 90179 | Lelio R Paula | 10/2012 |
9925 | 2^299550+189 | 90174 | Lelio R Paula | 10/2012 |
9926 | 10^90170+376063 | 90171 | Patrick De Geest | 07/2019 |
9927 | 10^90170-6749 | 90170 | Patrick De Geest | 09/2018 |
9928 | (2^299535+3)/29 | 90168 | Lelio R Paula | 01/2013 |
9929 | (2^299521+13)/15 | 90164 | Stefano Morozzi | 03/2020 |
9930 | 22316^10971+10971^22316 | 90163 | Hans Havermann | 08/2020 |
9931 | 10^90160+271947 | 90161 | Patrick De Geest | 07/2019 |
9932 | 10^90160-5613 | 90160 | Patrick De Geest | 09/2018 |
9933 | (97*10^90155-1)/3 | 90157 | Serge Batalov | 12/2014 |
9934 | (29*10^90153+583)/9 | 90154 | Robert Price | 06/2021 |
9936 | 3^188938+8680 | 90147 | Lelio R Paula | 04/2016 |
9935 | 10^90146+160209 | 90147 | Patrick De Geest | 07/2019 |
9937 | 10^90146-2027 | 90146 | Patrick De Geest | 09/2018 |
9938 | 6^115840-55 | 90142 | Lelio R Paula | 05/2016 |
9939 | (5*10^90142-473)/9 | 90142 | Robert Price | 12/2017 |
9940 | 8*7^106659+5 | 90139 | Lelio R Paula | 10/2014 |
9941 | 2^299406-16653 | 90131 | Enzo Doria | 05/2013 |
9942 | (317057^16384+1)/2 | 90131 | Richard Fischer | 10/2019 |
9943 | (2^299409+834)/2 | 90131 | Stefano Morozzi | 01/2020 |
9944 | 10^90128+288673 | 90129 | Patrick De Geest | 07/2019 |
9946 | 208049#+(216091#)/(208049#) | 90128 | Makoto Morimoto | 04/2016 |
9945 | 10^90128-8387 | 90128 | Patrick De Geest | 09/2018 |
9948 | (F(5)^128941-F(4)^128941)/F(3) | 90126 | Wayne Halsdorf | 03/2012 |
9947 | (5^128941-3^128941)/2 | 90126 | Kellen Shenton | 05/2022 |
9949 | 6^115819-53 | 90125 | Lelio R Paula | 05/2016 |
9950 | 10^90123+6313 | 90124 | Patrick De Geest | 09/2018 |
9951 | 6^115816-16853 | 90123 | Enzo Doria | 02/2013 |
9952 | 10^90123-22617 | 90123 | Patrick De Geest | 07/2019 |
9953 | 6^115813-23 | 90121 | Lelio R Paula | 05/2016 |
9954 | 2^299351-933075 | 90114 | Paul Bourdelais | 04/2021 |
9955 | (22*10^90110+161)/3 | 90111 | Robert Price | 02/2017 |
9957 | (2^299330-509203)/69 | 90106 | Lelio R Paula | 01/2013 |
9956 | 10^90105+915759 | 90106 | Patrick De Geest | 07/2019 |
9958 | 10^90105-767 | 90105 | Patrick De Geest | 09/2018 |
9959 | 10^90104+48189 | 90105 | Patrick De Geest | 07/2019 |
9960 | (6050^23827-1)/6049 | 90105 | Serge Batalov | 08/2020 |
9962 | 10^90104-7703 | 90104 | Patrick De Geest | 09/2018 |
9963 | 10^90103+9159 | 90104 | Patrick De Geest | 09/2018 |
9961 | (797*10^90102-23)/9 | 90104 | Robert Price | 01/2022 |
9964 | 10^90103-208457 | 90103 | Patrick De Geest | 07/2019 |
9965 | 10^90102+73011 | 90103 | Patrick De Geest | 07/2019 |
9966 | 10^90102-602433 | 90102 | Patrick De Geest | 07/2019 |
9967 | 10^90101+1225537 | 90102 | Patrick De Geest | 07/2019 |
9969 | 10^90101-3207 | 90101 | Patrick De Geest | 09/2018 |
9968 | 21730^14007+14007^21730 | 90101 | Hans Havermann | 08/2020 |
9970 | (29*10^90096-17)/3 | 90097 | Erik Branger | 09/2014 |
9971 | (49*10^90094+221)/9 | 90095 | Robert Price | 02/2022 |
9972 | 10^90089+143181 | 90090 | Patrick De Geest | 07/2019 |
9973 | 10^90089-3573 | 90089 | Patrick De Geest | 09/2018 |
9974 | 2^299247+1870529 | 90083 | Enzo Doria | 05/2016 |
9975 | 10^90079+1609 | 90080 | Patrick De Geest | 09/2018 |
9976 | 10^90079-230043 | 90079 | Patrick De Geest | 07/2019 |
9977 | 2^299229-2797783 | 90077 | Enzo Doria | 04/2016 |
9978 | 2^299220-16317 | 90075 | Enzo Doria | 04/2013 |
9979 | 11^86491-1350 | 90072 | Enzo Doria | 12/2012 |
9980 | 10^90071+52333 | 90072 | Patrick De Geest | 07/2019 |
9982 | 10^90071-1233 | 90071 | Patrick De Geest | 09/2018 |
9981 | (314401^16384+1)/2 | 90071 | Richard Fischer | 10/2019 |
9983 | 10^90069+158527 | 90070 | Patrick De Geest | 07/2019 |
9984 | 10^90069-7841 | 90069 | Patrick De Geest | 09/2018 |
9985 | (31*10^90064-1)/3 | 90066 | Robert Price | 03/2017 |
9986 | 10^90060+149431 | 90061 | Patrick De Geest | 07/2019 |
9987 | 10^90060-839 | 90060 | Patrick De Geest | 09/2018 |
9988 | 10^90052+2361 | 90053 | Patrick De Geest | 09/2018 |
9989 | 10^90052-90929 | 90052 | Patrick De Geest | 07/2019 |
9990 | 10^90047+619 | 90048 | Patrick De Geest | 09/2018 |
9991 | 10^90047-151071 | 90047 | Patrick De Geest | 07/2019 |
9992 | L(430949)/861899/1440387561539 | 90045 | Serge Batalov | 07/2017 |
9993 | 22996^8233+8233^22996 | 90043 | Hans Havermann | 08/2020 |
9994 | 2^299112+73951 | 90042 | Enzo Doria | 04/2016 |
9995 | 8^99702+7^(99702-1) | 90040 | Robert Price | 02/2016 |
9996 | 10^90038+157803 | 90039 | Patrick De Geest | 07/2019 |
9997 | 10^90038-9687 | 90038 | Patrick De Geest | 09/2018 |
9999 | 5*10^90033+3 | 90034 | Dmitry Domanov | 11/2010 |
9998 | (17574^21211-1)/17573 | 90034 | Serge Batalov | 08/2020 |
10000 | 10^90030+225813 | 90031 | Patrick De Geest | 07/2019 |